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Circles Quiz - CBSE Class 7 Mathematics

Free practice quiz: Circles (CBSE Class 7 Mathematics). 16 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 16 multiple-choice questions on Circles, and 16 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Basic parts of a circle

  • A circle is the set of all points at the same distance from a fixed point called the centre.
  • The radius joins the centre to the circle. The diameter passes through the centre and joins two points on the circle.
  • The boundary of the circle is called its circumference.
Diameter from radius
\[d = 2r\]
Radius from diameter
\[r = \frac{d}{2}\]

Common mistake: Mixing up radius and diameter. The diameter is twice the radius, not half of it.

Chords, secants, tangents and arcs

  • A chord joins any two points on a circle. The diameter is the longest chord.
  • A secant cuts the circle at two points. A tangent touches the circle at exactly one point.
  • An arc is a part of the circumference. A semicircle is half a circle, and the angle in a semicircle is a right angle.
Angle in a semicircle
\[\angle APB = 90^\circ \text{ when } AB \text{ is a diameter}\]

Common mistake: Confusing a secant with a chord. A chord is only the segment inside the circle, while a secant is a whole line.

Measuring a full turn

  • One complete turn around the centre of a circle measures 360 degrees.
  • Angles can also be measured in radians. A full turn equals 2π radians.
Full turn
\[360^\circ = 2\pi \text{ radians}\]
Half turn
\[180^\circ = \pi \text{ radians}\]

Common mistake: Thinking a full circle is π radians. π radians is only a half turn.

Circumference of a circle

  • The circumference is the distance around the circle. It is found by multiplying π by the diameter.
  • To find the radius from a given circumference, divide the circumference by 2π.
  • Circumferences are in the same ratio as their radii.
Circumference
\[C = 2\pi r = \pi d\]
Radius from circumference
\[r = \frac{C}{2\pi}\]
Ratio of circumferences
\[C_1 : C_2 = r_1 : r_2\]

Common mistake: Dividing the circumference by π only and calling the result the radius. That result is the diameter.

Area of circles and parts

  • Area is the space inside the circle. It equals π multiplied by the radius squared.
  • A semicircle has half the area of the full circle. A quarter circle has one-fourth of it.
  • To find the radius from an area, divide the area by π, then take the square root.
Area of a circle
\[A = \pi r^2\]
Radius from area
\[r = \sqrt{\frac{A}{\pi}}\]
Area of a semicircle
\[A = \frac{1}{2}\pi r^2\]
Area of a quarter circle
\[A = \frac{1}{4}\pi r^2\]

Common mistake: Forgetting to square the radius, or squaring the diameter instead of the radius.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the center point of a circle called?

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    Answer: A. Center

    The center point of a circle is called the Center.

  2. If a circle's radius is 4 cm, what is the diameter?

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    Answer: C. 8 cm

    The diameter is twice the radius; thus for 4 cm radius, the diameter is 8 cm.

  3. What do you call the longest chord in a circle?

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    Answer: C. Diameter

    The diameter is the longest chord in a circle, passing through the center.

  4. What is the angle formed in a semicircle?

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    Answer: C. 90°

    The angle formed in a semicircle is a right angle, which is 90°.

  5. If the circumference of a circle is 31.4 cm, what is the approximate radius? (π ≈ 3.14)

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    Answer: A. 5 cm

    Circumference is 2πr, solving 31.4 = 2 × 3.14 × r gives r ≈ 5 cm.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What defines the boundary of a circle?
  2. What is twice the radius of a circle called?
  3. Which segment connects any two points on a circle?
  4. What term is used for a line that cuts a circle at two points?
  5. Which part of the circle does not form part of a full circle?
  6. What term describes a line that touches a circle at exactly one point?
  7. How many degrees are in the total measure of a circle?
  8. How many radians are there in a full circle?
  9. Find the radius of a circle with an area of 314 cm². (π ≈ 3.14)
  10. If two circles have radii 5 cm and 12 cm, find the ratio of their circumferences.
  11. What is the area of a quarter circle with radius 7 cm? (π ≈ 3.14)

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